PRP Records

Probable Primes Top 10000

(253476 PRPs in the top)

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
9001(2^199949+6354)/260191Stefano Morozzi08/2019
9002(2^199946+11802)/260190Stefano Morozzi08/2019
9003(2^199947+31490)/260190Stefano Morozzi08/2019
9004(2^199923+31266)/260183Stefano Morozzi08/2019
9005(28*10^60180+149)/360181Robert Price10/2017
9006(2^199911+13346)/260179Stefano Morozzi08/2019
9007(2^199907+1470)/260178Stefano Morozzi07/2019
9008(2^199903+4406)/260177Stefano Morozzi08/2019
9009(2^199904+11998)/260177Stefano Morozzi08/2019
9010(2^199904+16038)/260177Stefano Morozzi08/2019
9011(2^199895+22994)/260175Stefano Morozzi08/2019
9012(2^199896+22582)/260175Stefano Morozzi08/2019
9013(2^199887+3914)/260172Stefano Morozzi08/2019
9014(2^199875+25926)/260169Stefano Morozzi08/2019
90162^199872+9360168Donovan Johnson06/2008
90156^77321+7760168Lelio R Paula04/2013
9017(86*10^60165-77)/960166Robert Price05/2016
9018(2^199860+31726)/260164Stefano Morozzi08/2019
9019(2^199855+714)/260163Stefano Morozzi07/2019
9020(2^199868+78557)/2337360162Lelio R Paula05/2012
9021(2^199848+33490)/260160Stefano Morozzi08/2019
9022(2^199838+13878)/260157Stefano Morozzi08/2019
90247^71180+8260155Lelio R Paula04/2013
9023(2^199830+32998)/260155Stefano Morozzi08/2019
90262^199814-11229560151Enzo Doria06/2014
9025(51^35227-1)/5060151Paul Bourdelais08/2017
9027(2^199812+31458)/260150Stefano Morozzi08/2019
9028(2^199807+31314)/260148Stefano Morozzi08/2019
9029(2^199796+19858)/260145Stefano Morozzi08/2019
9030(2^199792+30982)/260144Stefano Morozzi08/2019
9031(2^199794+24342)/260144Stefano Morozzi08/2019
9032(2^199788+16482)/260142Stefano Morozzi08/2019
9033(2^199778+12538)/260139Stefano Morozzi08/2019
9034(2^199773+33642)/260138Stefano Morozzi08/2019
9035(2^199774+16774)/260138Stefano Morozzi08/2019
903642964!3-8160135Robert Price09/2014
9037(2^199746+4714)/260130Stefano Morozzi08/2019
9038(2^199734+13798)/260126Stefano Morozzi08/2019
9039(2^199725+7710)/260123Stefano Morozzi08/2019
9040(2^199718+6822)/260121Stefano Morozzi08/2019
9041(2^199718+24690)/260121Stefano Morozzi08/2019
9042(2^199712+23790)/260120Stefano Morozzi08/2019
90432^199709-5160119Lelio R Paula05/2011
90442^199700-11162360116Enzo Doria05/2014
9045(15185*2^199681-1)/15960112Lelio R Paula04/2015
90462^199672+253360108Henri Lifchitz09/2004
904720^46198-1160105Lelio R Paula04/2013
9048(2^199665+25806)/260105Stefano Morozzi08/2019
9049(2^199662+6918)/260104Stefano Morozzi08/2019
90502^199657+9325760103Yves Minet03/2010
90513^125967-11060102Lelio R Paula10/2012
90522^199654-1881360102Enzo Doria05/2013
9053(29*10^60100+19)/360101Robert Price01/2017
9054(2^199627+31790)/260094Stefano Morozzi08/2019
9055(2^199619+19634)/260092Stefano Morozzi08/2019
90572^199615-2*199615+160091Robert Price04/2018
9056(2^199617+31166)/260091Stefano Morozzi08/2019
9058(2^199603+20510)/260087Stefano Morozzi08/2019
9059129^28468+28468^12960085Serge Batalov05/2014
9060(2^199591+16650)/260083Stefano Morozzi08/2019
9061(2^199587+3126)/260082Stefano Morozzi08/2019
9062(2^199581+27330)/260080Stefano Morozzi08/2019
9063(2^199578+11082)/260079Stefano Morozzi08/2019
90642^199572-1587360078Enzo Doria04/2013
9065(2^199568+25026)/260076Stefano Morozzi08/2019
9066(2^199569+3546)/260076Stefano Morozzi08/2019
90689*2^199559+760075Lelio R Paula03/2014
9067(2^199564+28906)/260075Stefano Morozzi08/2019
9069(2^199542+24118)/260068Stefano Morozzi08/2019
9070(2^199533+12674)/260066Stefano Morozzi08/2019
90712^199527-11191960064Enzo Doria05/2014
90722^199522+8287560063Lelio R Paula10/2012
90735^85928-7260062Lelio R Paula10/2012
907439^37749+3860062Norbert Schneider05/2014
90756^77182-14360060Lelio R Paula10/2012
9076(2^199514+15958)/260060Stefano Morozzi08/2019
9077(2^199507+28778)/260058Stefano Morozzi08/2019
9078(2^199508+21918)/260058Stefano Morozzi08/2019
90792^199502-214560057Lelio R Paula06/2011
90802^199493+425760054Lelio R Paula06/2011
9081(2^199492+7150)/260053Stefano Morozzi08/2019
90832^199488+4075560052Lelio R Paula06/2011
9082(2^199487+4134)/260052Stefano Morozzi08/2019
9084(2^199481+16494)/260050Stefano Morozzi08/2019
9085(2^199478+9550)/260049Stefano Morozzi08/2019
9086(2^199465+954)/260045Stefano Morozzi07/2019
9087(2^199445+29586)/260039Stefano Morozzi08/2019
9089(2^199451+9)/2561960037Lelio R Paula02/2012
9088(2^199439+21494)/260037Stefano Morozzi08/2019
90902^199425-6160033Lelio R Paula05/2011
9091(85*10^60026+23)/960027Robert Price11/2015
9092(2^199403+1470)/260026Stefano Morozzi07/2019
9093(2^199400+22162)/260026Stefano Morozzi08/2019
9094(2^199402+22182)/260026Stefano Morozzi08/2019
9095(2^199392+12342)/260023Stefano Morozzi08/2019
9096(2^199389+13266)/260022Stefano Morozzi08/2019
909965^33107+6260021Lelio R Paula01/2016
9097(2^199386+8590)/260021Stefano Morozzi08/2019
9098(2^199384+22686)/260021Stefano Morozzi08/2019
9100(2^199381+29366)/260020Stefano Morozzi08/2019
9101(2^199377+5882)/260019Stefano Morozzi08/2019
9102(2^199377+20414)/260019Stefano Morozzi08/2019
9103(2^199371+29426)/260017Stefano Morozzi08/2019
91052^199362-121560014Lelio R Paula06/2011
91042^199362-11163360014Enzo Doria05/2014
91061537^18832+18832^153760012Serge Batalov05/2014
9107(2^199352+4218)/260011Stefano Morozzi08/2019
9108(2^199329+974)/260004Stefano Morozzi07/2019
9109(2^199329+21386)/260004Stefano Morozzi08/2019
91102^199324-1743360003Enzo Doria05/2013
911110^60000+20433160001Milton L. Brown04/2006
911210^60000+8712960001Milton L. Brown04/2006
9113143^27838-260001Lelio R Paula10/2017
912710^59999+6519760000Patrick De Geest04/2005
914810^60000-3252960000Patrick De Geest08/2009
9128(10^60000+2249)/960000Makoto Morimoto09/2016
9129((2^43112609)/10^24296)%10^6000060000Michael Vang10/2016
9130(2^57885161/10^105090)%10^6000060000Michael Vang10/2016
9131(2^42643801/10^58945)%10^6000060000Michael Vang10/2016
9114(2^37156667/10^243655)%10^6000060000Michael Vang10/2016
9115(2^30402457/10^69028)%10^6000060000Michael Vang11/2016
9116(2^32582657/10^248088)%10^6000060000Michael Vang11/2016
9117(2^32582657/10^238942)%10^6000060000Michael Vang11/2016
9118(2^24036583/10^13547)%10^6000060000Michael Vang11/2016
9119(2^20996011/10^131008)%10^6000060000Michael Vang11/2016
9120(2^13466917/10^79774)%10^6000060000Michael Vang11/2016
9121(2^13466917/10^102581)%10^6000060000Michael Vang11/2016
9122(2^6972593/10^339640)%10^6000060000Michael Vang11/2016
9123(2^2976221/10^65464)%10^6000060000Michael Vang12/2016
9124(2^1398269/10^61138)%10^6000060000Michael Vang12/2016
9125(2^3021377/10^418881)%10^6000060000Michael Vang12/2016
9126(2^1257787/10^164080)%10^6000060000Michael Vang12/2016
91322^199313-22567560000Stefano Morozzi05/2019
91332^199313-32690160000Stefano Morozzi05/2019
91342^199313-53217160000Stefano Morozzi05/2019
91352^199313-63285160000Stefano Morozzi05/2019
91362^199313-82528960000Stefano Morozzi05/2019
91372^199313-85769160000Stefano Morozzi05/2019
91382^199313+8370560000Stefano Morozzi05/2019
91392^199313+17543960000Stefano Morozzi05/2019
91402^199313+40171560000Stefano Morozzi05/2019
91412^199313+41836760000Stefano Morozzi05/2019
91422^199313+52051760000Stefano Morozzi05/2019
91432^199313+58297560000Stefano Morozzi05/2019
91442^199313+60032960000Stefano Morozzi05/2019
91452^199313+60116160000Stefano Morozzi05/2019
91462^199313+60146760000Stefano Morozzi05/2019
91472^199313+92970560000Stefano Morozzi05/2019
915810^59999-51626759999Patrick De Geest06/2009
915020^46116-4159999Lelio R Paula03/2013
9159(2^74207281/10^184638)%10^6000059999Michael Vang10/2016
9149(2^25964951/10^135429)%10^6000059999Michael Vang11/2016
9151(2^199313+804446)/259999Stefano Morozzi06/2019
9152(2^199313+885410)/259999Stefano Morozzi06/2019
9153(2^199313+916374)/259999Stefano Morozzi06/2019
9154(2^199313+501865)/359999Stefano Morozzi06/2019
9155(2^199313+979327)/359999Stefano Morozzi06/2019
9156(2^199313+870498)/1059999Stefano Morozzi06/2019
9157(2^199311+25154)/259999Stefano Morozzi08/2019
9160(2^199313+911951)/5359998Stefano Morozzi06/2019
9161(2^199313+622557)/5959998Stefano Morozzi06/2019
9162(2^199313+548359)/11159998Stefano Morozzi06/2019
9163(2^199313+881010)/14259998Stefano Morozzi06/2019
9164(2^199307+518)/259998Stefano Morozzi07/2019
9165(2^199313+20613)/41559997Stefano Morozzi06/2019
9166(2^199313+846966)/15859997Stefano Morozzi06/2019
9167(2^199313+689239)/21359997Stefano Morozzi06/2019
9168(2^199313+792637)/30359997Stefano Morozzi06/2019
9169(2^199313+979299)/73359997Stefano Morozzi06/2019
9170(2^199313+760551)/148159997Stefano Morozzi06/2019
9171(2^199305+1010)/259997Stefano Morozzi07/2019
91746^77100-5559996Lelio R Paula10/2012
9172(2^199313+8825)/773359996Stefano Morozzi06/2019
9173(2^199313+621926)/159859996Stefano Morozzi06/2019
9175(2^199300+490)/259995Stefano Morozzi07/2019
9176(2^199296+30726)/259994Stefano Morozzi08/2019
9177(2^199284+21562)/259991Stefano Morozzi08/2019
9178(2^199280+29442)/259989Stefano Morozzi08/2019
9179(2^199313+17227)/146774187977159988Stefano Morozzi06/2019
9182(19*2^199274+1)/16159987Lelio R Paula07/2012
9181(23^44053+1)/2459987Robert Price06/2013
9180(2^199313+30419)/195223029100759987Stefano Morozzi06/2019
9183(2^199264+22782)/259985Stefano Morozzi08/2019
9184(2^199313+4605)/776935587940608759984Stefano Morozzi06/2019
9185(2^199313+47559)/783044506792936959984Stefano Morozzi06/2019
9186(2^199261+22866)/259984Stefano Morozzi08/2019
9187(2^199313+16238)/70962375306317203059982Stefano Morozzi06/2019
9188(2^199238+9510)/259977Stefano Morozzi08/2019
9189(2^199234+21822)/259976Stefano Morozzi08/2019
91909^62848+6^62848-2^6284859973Mike Oakes08/2010
9191(2^199217+27566)/259970Stefano Morozzi08/2019
9192(2^199213+24042)/259969Stefano Morozzi08/2019
9193(2^199201+21666)/259966Stefano Morozzi08/2019
919411438^14775-14775^1143859963Norbert Schneider05/2019
919615852^6061+6061^1585259961Hans Havermann08/2016
9195(2^199185+7686)/259961Stefano Morozzi08/2019
9197(2^199167+16070)/259955Stefano Morozzi08/2019
9198(2^199153+2586)/259951Stefano Morozzi08/2019
9199(2^199148+29058)/259950Stefano Morozzi08/2019
920019^46880-2059948Lelio R Paula03/2013
9201(2^199132+32682)/259945Stefano Morozzi08/2019
9202(2^199129+21242)/259944Stefano Morozzi08/2019
9203(2^199115+31418)/259940Stefano Morozzi08/2019
92042^199107-1773759938Enzo Doria05/2013
9205(2^199093+4770)/259933Stefano Morozzi08/2019
9206(2^199089+13070)/259932Stefano Morozzi08/2019
9209(13*10^59928+83)/359929Robert Price09/2016
9207(2^199078+26338)/259929Stefano Morozzi08/2019
9208(2^199079+11066)/259929Stefano Morozzi08/2019
9210(2^199070+10998)/259926Stefano Morozzi08/2019
9211(2^199060+29022)/259923Stefano Morozzi08/2019
9212(2^199043+9618)/259918Stefano Morozzi08/2019
9213(2^199043+14550)/259918Stefano Morozzi08/2019
921410^59913+10893143159914Marisa Kirisame02/2015
921510^59913+4861959914Patrick De Geest04/2016
921610^59913-7412359913Patrick De Geest03/2016
9217(2^199024+9450)/259912Stefano Morozzi08/2019
9218(2^199015+2258)/259910Stefano Morozzi08/2019
9219(2^199017+6282)/259910Stefano Morozzi08/2019
922010611^14878-14878^1061159896Norbert Schneider07/2019
9221t(199528)59890Robert Price01/2015
92222^198903-1790159876Enzo Doria05/2013
92239*10^59862-1959863Robert Price10/2017
9224gcd(V(776555),5*F(155311)*(F(155311)+1)+1)59858Serge Batalov04/2015
9225(3^125447+7)/259854Lelio R Paula04/2012
92265^85630+4^(85630-1)59853Robert Price03/2016
92272^198824-213559852Yves Minet06/2013
9228(124^28591-1)/12359851Richard Fischer10/2017
92292^198799-1611759845Enzo Doria04/2013
92307^70811+6^(70811+1)59843Robert Price07/2016
92312^198774-1594559837Enzo Doria04/2013
92322^198753-1587359831Enzo Doria04/2013
9233(31*2^198748-1)/4559829Lelio R Paula01/2014
92342^198725+6959823Lelio R Paula04/2011
9235(68*10^59821+31)/959822Robert Price10/2015
9236(37*25^42785+1867)/859812Curtis Bright05/2015
92383^125354+266059810Lelio R Paula10/2012
9237105^29591-10459810Norbert Schneider08/2013
92394*5^85565-359808Lelio R Paula09/2014
924013963842222*Bern(19550)/5572727559803Thomas Ritschel03/2014
9242125330^3+3^12533059798Anatoly F. Selevich06/2010
92412^198643-318959798Yves Minet10/2014
9243(13*10^59797+191)/359798Robert Price08/2017
9244(7*10^59796-1)/359797Erik Branger03/2014
92452^198595+15359784Lelio R Paula04/2011
9246(19*10^59766+161)/959767Robert Price07/2016
92472^198510-196559758Lelio R Paula06/2011
92482^198506-1907759757Enzo Doria05/2013
92492^198484-1600559750Enzo Doria04/2013
92502^198473-1682159747Enzo Doria05/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

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